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Montague grammar is an approach to natural language semantics,
based on formal logic, especially lambda calculus and set theory.
Montague grammar was named after American logician Richard Montague,
who pioneered this approach in the 1960s and early 1970s.
Montague's thesis was that there is no essential difference between the semantics of natural languages (like English) and formal languages (like predicate logic).
Montague's treatment of quantification has been linked to the notion of continuation
in programming language semantics. (See
Continuations in Natural Language (http://www.cs.bham.ac.uk/~hxt/cw04/barker.pdf).)
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